Welcome to the second installment in my series, “Top 10 Things to Know About Economics.” The first was not all that well-received, because it turns it out it was just too dense with equations (it didn’t help that the equation formatting was a pain.) Fortunately I think I can explain monopoly and oligopoly with far fewer equations—which I will represent as PNG for your convenience.

You probably already know at least in basic terms how a monopoly works: When there is only one seller of a product, that seller can charge higher prices. But did you ever stop and think about why they can charge higher prices—or why they’d want to?

The latter question is not as trivial as it sounds; higher prices don’t necessarily mean higher profits. By the Law of Demand (which, like the Pirate Code, is really more like a guideline), raising the price of a product will result in fewer being sold. There are two countervailing effects: Raising the price raises the profits from selling each item, but reduces the number of items sold. The optimal price, therefore, is the one that balances these two effects, maximizing price times quantity.

A monopoly can actually set this optimal price (provided that they can figure out what it is, of course; but let’s assume they can). They therefore solve this maximization problem for price P(Q) a function of quantity sold, quantity Q, and cost C(Q) a function of quantity produced (which at the optimum is equal to quantity sold; no sense making them if you won’t sell them!):

As you may remember if you’ve studied calculus, the maximum is achieved at the point where the derivative is zero. If you haven’t studied calculus, the basic intuition here is that you move along the curve seeing whether the profits go up or down with each small change, and when you reach the very top—the maximum—you’ll be at a point where you switch from going up to going down, and at that exact point a small change will move neither up nor down. The derivative is really just a fancy term for the slope of the curve at each point; at a maximum this slope changes from positive to negative, and at the exact point it is zero.

This is a general solution, but it’s easier to understand if we use something more specific. As usual, let’s make things simpler by assuming everything is linear; we’ll assume that demand starts at a maximum price of P0 and then decreases at a rate 1/e. This is the demand curve.

Then, we’ll assume that the marginal cost of production C'(Q) is also linear, increasing at a rate 1/n. This is the supply curve.

Now we can graph the supply and demand curves from these equations. But the monopoly doesn’t simply set supply equal to demand; instead, they set supply equal to marginal revenue, which takes into account the fact that selling more items requires lowering the price on all of them. Marginal revenue is this term:

This is strictly less than the actual price, because increasing the quantity sold requires decreasing the price—which means that P'(Q) < 0. They set the quantity by setting marginal revenue equal to marginal cost. Then they set the price by substituting that quantity back into the demand equation.

Thus, the monopoly should set this quantity:

They would then charge this price (substitute back into the demand equation):

On a graph, there are the supply and demand curves, and then below the demand curve, the marginal revenue curve; it’s the intersection of that curve with the supply curve that the monopoly uses to set its quantity, and then it substitutes that quantity into the demand curve to get the price:

Now I’ll show that this is higher than the price in a perfectly competitive market. In a competitive market, competitive companies can’t do anything to change the price, so from their perspective P'(Q) = 0. They can only control the quantity they produce and sell; they keep producing more as long as they receive more money for each one than it cost to produce it. By the Law of Diminishing Returns (again more like a guideline) the cost will increase as they produce more, until finally the last one they sell cost just as much to make as they made from selling it. (Why bother selling that last one, you ask? You’re right; they’d actually sell one less than this, but if we assume that we’re talking about thousands of products sold, one shouldn’t make much difference.)

Price is simply equal to marginal cost:

In our specific linear case that comes out to this quantity:

Therefore, they charge this price (you can substitute into either the supply or demand equations, because in a competitive market supply equals demand):

Subtract the two, and you can see that monopoly price is higher than the competitive price by this amount:

Notice that the monopoly price will always be larger than the competitive price, so long as e > 0 and n > 0, meaning that increasing the quantity sold requires decreasing the price, but increasing the cost of production. A monopoly has an incentive to raise the price higher than the competitive price, but not too much higher—they still want to make sure they sell enough products.

Monopolies introduce deadweight loss, because in order to hold the price up they don’t produce as many products as people actually want. More precisely, each new product produced would add overall value to the economy, but the monopoly stops producing them anyway because it wouldn’t add to their own profits.

One “solution” to this problem is to let the monopoly actually take those profits; they can do this if they price-discriminate, charging a higher price for some customers than others. In the best-case scenario (for them), they charge each customer a price that they are just barely willing to pay, and thus produce until no customer is willing to pay more than the product costs to make. That final product sold also has price equal to marginal cost, so the total quantity sold is the same under competition. It is, in that sense, “efficient”.

What many neoclassical economists seem to forget about price-discriminating monopolies is that they appropriate the entire surplus value of the product—the customers are only just barely willing to buy; they get no surplus value from doing so.

In reality, very few monopolies can price-discriminate that precisely; instead, they put customers into broad categories and then try to optimize the price for each of those categories. Credit ratings, student discounts, veteran discounts, even happy hours are all forms of this categorical price discrimination. If the company cares even a little bit about what sort of customer you are rather than how much money you’re paying, they are price-discriminating.

It’s so ubiquitous I’m actually having trouble finding a good example of a product that doesn’t have categorical price discrimination. I was thinking maybe computers? Nope, student discounts. Cars? No, employee discounts and credit ratings. Refrigerators, maybe? Well, unless there are coupons (coupons price discriminate against people who don’t want to bother clipping them). Certainly not cocktails (happy hour) or haircuts (discriminationby sex, the audacity!); and don’t even get me started on software.

I introduced price-discrimination in the context of monopoly, which is usually how it’s done; but one thing you’ll notice about all the markets I just indicated is that they aren’t monopolies, yet they still exhibit price discrimination. Cars, computers, refrigerators, and software are made under oligopoly, a system in which a handful of companies control the majority of the market. As you might imagine, an oligopoly tends to act somewhere in between a monopoly and a competitive market—but there are some very interesting wrinkles I’ll get to in a moment.

Cocktails and haircuts are sold in a different but still quite interesting system called monopolistic competition; indeed, I’m not convinced that there is any other form of competition in the real world. True perfectly-competitive markets just don’t seem to actually exist. Under monopolistic competition, there are many companies that don’t have much control over price in the overall market, but the products they sell aren’t quite the same—they’re close, but not equivalent. Some barbers are just better at cutting hair, and some bars are more fun than others. More importantly, they aren’t the same for everyone. They have different customer bases, which may overlap but still aren’t the same. You don’t just want a barber who is good, you want one who works close to where you live. You don’t just want a bar that’s fun; you want one that you can stop by after work. Even if you are quite discerning and sensitive to price, you’re not going to drive from Ann Arbor to Cleveland to get your hair cut—it would cost more for the gasoline than the difference. And someone is Cleveland isn’t going to drive all the way to Ann Arbor, either! Hence, barbers in Ann Arbor have something like a monopoly (or oligopoly) over Ann Arbor haircuts, and barbers in Cleveland have something like a monopoly over Cleveland haircuts. That’s monopolistic competition.

Supposedly monopolistic competition drives profits to zero in the long run, but I’ve yet to see this happen in any real market. Maybe the problem is that conceit “the long run”; as Keynes said, “in the long run we are all dead.” Sometimes the argument is made that it has driven real economic profits to zero, because you’ve got to take into account the cost of entry, the normal profit. But of course, that’s extremely difficult to measure, so how do we know whether profits have been driven to normal profit? Moreover, the cost of entry isn’t the same for everyone, so people with lower cost of entry are still going to make real economic profits. This means that the majority of companies are going to still make some real economic profit, and only the ones that had the hardest time entering will actually see their profits driven to zero.

Monopolistic competition is relatively simple. Oligopoly, on the other hand, is fiercely complicated. Why? Because under oligopoly, you actually have to treat human beings as human beings.

What I mean by that is that under perfect competition or even monopolistic competition, the economic incentives are so powerful that people basically have to behave according to the neoclassical rational agent model, or they’re going to go out of business. There is very little room for errors or even altruistic acts, because your profit margin is so tight. In perfect competition, there is literally zero room; in monopolistic competition, the only room for individual behavior is provided by the degree of monopoly, which in most industries is fairly small. One person’s actions are unable to shift the direction of the overall market, so the market as a system has ultimate power.

Under oligopoly, on the other hand, there are a handful of companies, and people know their names. You as a CEO have a reputation with customers—and perhaps more importantly, a reputation with other companies. Individual decision-makers matter, and one person’s decision depends on their prediction of other people’s decision. That means we need game theory.

The simplest case is that of duopoly, where there are only two major companies. Not many industries are like this, but I can think of three: soft drinks (Coke and Pepsi), commercial airliners (Boeing and Airbus), and home-user operating systems (Microsoft and Apple). In all three cases, there is also some monopolistic element, because the products they sell are not exactly the same; but for now let’s ignore that and suppose they are close enough that nobody cares.

Imagine yourself in the position of, say, Boeing: How much should you charge for an airplane?

If Airbus didn’t exist, it’s simple; you’d charge the monopoly price. But since they do exist, the price you charge must depend not only on the conditions of the market, but also what you think Airbus is likely to do—and what they are likely to do depends in turn on what they think you are likely to do.

If you think Airbus is going to charge the monopoly price, what should you do? You could charge the monopoly price as well, which is called collusion. It’s illegal to actually sign a contract with Airbus to charge that price (though this doesn’t seem to stop cable companies or banks—probably has something to do with the fact that wenever punish them for doing it), and let’s suppose you as the CEO of Boeing are an honest and law-abiding citizen (I know, it’s pretty fanciful; I’m having trouble keeping a straight face myself) and aren’t going to violate the antitrust laws. You can still engage in tacit collusion, in which you both charge the monopoly price and take your half of the very high monopoly profits.

There’s a temptation not to collude, however, which the airlines who buy your planes are very much hoping you’ll succumb to. Suppose Airbus is selling their A350-100 for $341 million. You could sell the comparable 777-300ER for $330 million and basically collude, or you could cut the price and draw in more buyers. Say you cut it to $250 million; it probably only costs $150 million to make, so you’re still making a profit on each one; but where you sold say 150 planes a year and profited $180 million on each (a total profit of $27 billion), you could instead capture the whole market and sell 300 planes a year and profit $100 million on each (a total profit of $30 billion). That’s a 10% higher profit and $3 billion a year for your shareholders; why wouldn’t you do that?

Well, think about what will happen when Airbus releases next year’s price list. You cut the price to $250 million, so they retaliate by cutting their price to $200 million. Next thing you know, you’re cutting your own price to $150.1 million just to stay in the market, and they’re doing the same. When the dust settles, you still only control half the market, but now you profit a mere $100,000 per airplane, making your total profits a measly $15 million instead of $27 billion—that’s $27,000 million.(I looked it up, and as it turns out, Boeing’s actual gross profit is about $14 billion, so I underestimated the real cost of each airplane—but they’re clearly still colluding.) For a gain of 10% in one year you’ve paid a loss of 99.95% indefinitely. The airlines will be thrilled, and they’ll likely pass on much of those savings to their customers, who will fly more often, engage in more tourism, and improve the economy in tourism-dependent countries like France and Greece, so the worldmay well be better off. But you as CEO of Boeing don’t care about the world; you care about the shareholders of Boeing—and the shareholders of Boeing just got hosed. Don’t expect to keep your seat in the next election.

But now, suppose you think that Airbus is planning on setting a price of $250 million next year anyway. They should know you’ll retaliate, but maybe their current CEO is retiring next year and doesn’t care what happens to the company after that or something. Or maybe they’re just stupid or reckless. In any case, your sources (which, as an upstanding citizen, obviously wouldn’t include any industrial espionage!) tell you that Airbus is going to charge $250 million next year.

Well, in that case there’s no point in you charging $330 million; you’ll lose the market and look like a sucker. You could drop to $250 million and try to set up a new, lower collusive equilibrium; but really what you want to do is punish them severely for backstabbing you. (After all, human beings are particularly quick to anger when we perceive betrayal. So maybe you’ll charge $200 million and beat them at their own conniving game.

The next year, Airbus has a choice. They could raise back to $341 million and give you another year of big profits to atone for their reckless actions, or they could cut down to $180 million and keep the price war going. You might think that they should continue the war, but that’s short-term thinking; in the long run their best strategy is to atone for their actions and work to restore the collusion. In response, Boeing’s best strategy is to punish them when they break the collusion, but not hold a grudge; if they go back to the high price, Boeing should as well. This very simple strategy is called tit-for-tat, and it is utterly dominant in every simulation we’ve ever tried of this situation, which is technically called an iterated prisoner’s dilemma.

What if there are more than two companies involved? Then things get even more complicated, because now we’re dealing with things like what A’s prediction of what B predicts that C will predict A will do. In general this is a situation we only barely understand, and I think it is a topic that needs considerably more research than it has received.

There is an interesting simple model that actually seems to capture a lot about how oligopolies work, but no one can quite figure out why it works. That model is called Cournot competition. It assumes that companies take prices and fixed and compete by selecting the quantity they produce at each cycle. That’s incredibly bizarre; it seems much more realistic to say that they compete by setting prices. But if you do that, you get Bertrand competition, which requires us to go through that whole game-theory analysis—but now with three, or four, or ten companies!

Under Cournot competition, you decide how much to produce Q1 by monopolizing what’s left over after the other companies have produced their quantities Q2, Q3, and so on. If there are k companies, you optimize under the constraint that (k-1)Q2 has already been produced.

Let’s use our linear models again. Here, the quantity that goes into figuring the price is the total quantity, which is Q1+(k-1)Q2; while the quantity you sell is just Q1. But then, another weird part is that for the marginal cost function we use the whole market—maybe you’re limited by some natural resource, like oil or lithium?

It’s not as important for you to follow along with the algebra, though here you go if you want:

Then the key point is that the situation is symmetric, so Q1 = Q2 = Q3 = Q. Then the total quantity produced, which is what consumers care about, is kQ. That’s what sets the actual price as well.

My name is Patrick Julius. I am about halfway through a master’s degree in economics, specializing in the new subfield of cognitive economics (closely related to the also quite new fields of cognitive science and behavioral economics). This makes me in one sense heterodox; I disagree adamantly with most things that typical neoclassical economists say. But in another sense, I am actually quite orthodox. All I’m doing is bringing the insights of psychology, sociology, history, and political science—not to mention ethics—to the study of economics. The problem is simply that economists have divorced themselves so far from the rest of social science.

Another way I differ from most critics of mainstream economics (I’m looking at you, Peter Schiff) is that, for lack of a better phrase, I’m good at math. (As Bill Clinton said, “It’s arithmetic!”) I understand things like partial differential equations and subgame perfect equilibria, and therefore I am equipped to criticize them on their own terms. In this blog I will do my best to explain the esoteric mathematical concepts in terms most readers can understand, but it’s not always easy. The important thing to keep in mind is that fancy math can’t make a lie true; no matter how sophisticated its equations, a model that doesn’t fit the real world can’t be correct.

This blog, which I plan to update every Saturday, is about the current state of economics, both as it is and how economists imagine it to be. One of my central points is that these two are quite far apart, which has exacerbated if not caused the majority of economic problems in the world today. (Economists didn’t invent world hunger, but for over a decade now we’ve had the power to end it and haven’t done so. You’d be amazed how cheap it would be; we’re talking about 1% of First World GDP at most.)

The reason I call it “infinite identical psychopaths” is that this is what neoclassical economists appear to believe human beings are, at least if we judge by the models they use. These are the typical assumptions of a neoclassical economic model:

Perfect information: All individuals know everything they need to know about the state of the world and the actions of other individuals.

Rational expectations: Predictions about the future can only be wrong within a normal distribution, and in the long run are on average correct.

Representative agents: All individuals are identical and interchangeable; a single type represents them all.

Perfect competition: There are infinitely many agents in the market, and none of them ever collude with one another.

“Economic rationality”: Individuals act according to a monotonic increasing utility function that is only dependent upon their own present and future consumption of goods.

I put the last one in scare quotes because it is the worst of the bunch. What economists call “rationality” has only a distant relation to actual rationality, either as understood by common usage or by formal philosophical terminology.

Don’t be scared by the terminology; a “utility function” is just a formal model of the things you care about when you make decisions. Things you want have positive utility; things you don’t want have negative utility. Larger numbers reflect stronger feelings: a bar of chocolate has much less positive utility than a decade of happy marriage; a pinched finger has much less negative utility than a year of continual torture. Utility maximization just means that you try to get the things you want and avoid the things you don’t. By talking about expected utility, we make some allowance for an uncertain future—but not much, because we have so-called “rational expectations”.

Since any action taken by an “economically rational” agent maximizes expected utility, it is impossible for such an agent to ever make a mistake in the usual sense. Whatever they do is always the best idea at the time. This is already an extremely strong assumption that doesn’t make a whole lot of sense applied to human beings; who among us can honestly say they’ve never done anything they later regretted?

The worst part, however, is the assumption that an individual’s utility function depends only upon their own consumption. What this means is that the only thing anyone cares about is how much stuff they have; considerations like family, loyalty, justice, honesty, and fairness cannot factor into their decisions. The “monotonic increasing” part means that more stuff is always better; if they already have twelve private jets, they’d still want a thirteenth; and even if children had to starve for it, they’d be just fine with that. They are, in other words, psychopaths. So that’s one word of my title.

I think “identical” is rather self-explanatory; by using representative agent models, neoclassicists effectively assume that there is no variation between human beings whatsoever. They all have the same desires, the same goals, the same capabilities, the same resources. Implicit in this assumption is the notion that there is no such thing as poverty or wealth inequality, not to mention diversity, disability, or even differences in taste. (One wonders why you’d even bother with economics if that were the case.)

As for “infinite”, that comes from the assumptions of perfect information and perfect competition. In order to really have perfect information, one would need a brain with enough storage capacity to contain the state of every particle in the visible universe. Maybe not quite infinite, but pretty darn close. Likewise, in order to have true perfect competition, there must be infinitely many individuals in the economy, all of whom are poised to instantly take any opportunity offered that allows them to make even the tiniest profit.

Now, you might be thinking this is a strawman; surely neoclassicists don’t actually believe that people are infinite identical psychopaths. They just model that way to simplify the mathematics, which is of course necessary because the world is far too vast and interconnected to analyze in its full complexity.

This is certainly true: Suppose it took you one microsecond to consider each possible position on a Go board; how long would it take you to go through them all? More time than we have left before the universe fades into heat death. A Go board has two colors (plus empty) and 361 spaces. Now imagine trying to understand a global economy of 7 billion people by brute-force analysis. Simplifying heuristics are unavoidable.

And some neoclassical economists—for example Paul Krugman and Joseph Stiglitz—generally use these heuristics correctly; they understand the limitations of their models and don’t apply them in cases where they don’t belong. In that sort of case, there’s nothing particularly bad about these simplifying assumptions; they are like when a physicist models the trajectory of a spacecraft by assuming frictionless vacuum. Since outer space actually is close to a frictionless vacuum, this works pretty well; and if you need to make minor corrections (like the Pioneer Anomaly) you can.

However, this explanation already seems weird for the “economically rational” assumption (the psychopath part), because that doesn’t really make things much simpler. Why would we exclude the fact that people care about each other, they like to cooperate, they have feelings of loyalty and trust? And don’t tell me it’s because that’s impossible to quantify; behavioral geneticists already have a simple equation (C < r B) designed precisely to quantify altruism. (C is cost, B is benefit, r is relatedness.) I’d make only one slight modification; instead of r for relatedness, use pfor psychological closeness, or as I like to call it, solidarity. For humans, solidarity is usually much higher than relatedness, though the two are correlated. C < p B.

Worse, there are other neoclassical economists—those of the most fanatically “free-market” bent—who really don’t seem to do this. I don’t know if they honestly believe that people are infinite identical psychopaths, but they make policy as if they did.

These kinds of statements would only make sense if markets were really as efficient and competitive as neoclassical models—that is, if people were infinite identical psychopaths. Allow even a single monopoly or just a few bits of imperfect information, and that whole edifice collapses.

And indeed if you’ve ever been unemployed or known someone who was, you know that our labor markets just ain’t that efficient. If you want to cut unemployment payments, you need a better argument than that. Similarly, it’s obvious to anyone who isn’t wearing the blinders of economic ideology that many large corporations exert monopoly power to increase their profits at our expense (How can you not see that Apple is a monopoly!?).

This sort of reasoning is more like plotting the trajectory of an aircraft on the assumption of frictionless vacuum; you’d be baffled as to where the oxidizer comes from, or how the craft manages to lift itself off the ground when the exhaust vents are pointed sideways instead of downward. And then you’d be telling the aerospace engineers to cut off the wings because they’re useless mass.

Worst of all, if we continue this analogy, the engineers would listen to you—they’d actually be convinced by your differential equations and cut off the wings just as you requested. Then the plane would never fly, and they’d ask if they could put the wings back on—but you’d adamantly insist that it was just coincidence, you just happened to be hit by a random problem at the very same moment as you cut off the wings, and putting them back on will do nothing and only make things worse.

Can otherwise intelligent people really believe that these insane models are true? I’m not sure.
Sadly I think they may really believe that all people are psychopaths—because they themselves may be psychopaths. Economics students score higher on various psychopathic traits than other students. Part of this is self-selection—psychopaths are more likely to study economics—but the terrifying part is that part of it isn’t—studying economics may actually make you more like a sociopath. As I study for my master’s degree, I actually am somewhat afraid of being corrupted by this; I make sure to periodically disengage from their ideology and interact with normal people with normal human beliefs to recalibrate my moral compass.

Of course, it’s still pretty hard to imagine that anyone could honestly believe that the world economy is in a state of perfect information. But if they can’t really believe this insane assumption, why do they keep using models based on it?

The more charitable possibility is that they don’t appreciate just how sensitive the models are to the assumptions. They may think, for instance, that the General Welfare Theorems still basically apply if you relax the assumption of perfect information; maybe it’s not always Pareto-efficient, but it’s probably most of the time, right? Or at least close? Actually, no. The Myerson-Satterthwaithe Theorem says that once you give up perfect information, the whole theorem collapses;even a small amount of asymmetric information is enough to make it so that a Pareto-efficient outcome is impossible. And as you might expect, the more asymmetric the information is, the further the result deviates from Pareto-efficiency. And since we always have some asymmetric information, it looks like the General Welfare Theorems really aren’t doing much for us. They apply only in a magical fantasy world. (In case you didn’t know, Pareto-efficiency is a state in which it’s impossible to make any person better off without making someone else worse off. The real world is in a not Pareto-efficient state, which means that by smarter policy we could improve some people’s lives without hurting anyone else.)

The more sinister possibility is that they know full well that the models are wrong, they just don’t care. The models are really just excuses for an underlying ideology, the unshakeable belief that rich people are inherently better than poor people and private corporations are inherently better than governments. Hence, it must be bad for the economy to raise the minimum wage and good to cut income taxes, even though the empirical evidence runs exactly the opposite way; it must be good to subsidize big oil companies and bad to subsidize solar power research, even though that makes absolutely no sense.

No neoclassical model says that you should privatize prisons; prisons are a classic example of a public good, which would be underfunded in a competitive market and basically has to be operated or funded by the government.

No neoclassical model would support the idea that the EPA is a terrorist organization (yes, a member of the US Congress said this). In fact, the economic case for environmental regulations is unassailable. (What else are we supposed to do, privatize the air?) The question is not whether to regulate and tax pollution, but how and how much.

No neoclassical model says that you should deregulate finance; in fact, most neoclassical models don’t even include a financial sector (as bizarre and terrifying as that is), and those that do generally assume it is in a state of perfect equilibrium with zero arbitrage. If the financial sector were actually in a state of zero arbitrage, no banks would make a profit at all.

In case you weren’t aware, arbitrage is the practice of making money off of money without actually making any goods or doing any services. Unlike manufacturing (which, oddly enough, almost all neoclassical models are based on—despite the fact that it is now a minority sector in First World GDP), there’s no value added. Under zero arbitrage, the interest rate a bank charges should be almost exactly the same as the interest rate it receives, with just enough gap between to barely cover their operating expenses—which should in turn be minimal, especially in a modern electronic system. If financial markets were at zero arbitrage equilibrium, it would be sensible to speak of a single “real interest rate” in the economy, the one that everyone pays and everyone receives. Of course, those of us who live in the real world know that not only do different people pay radically different rates, most people have multiple outstanding lines of credit, each with a different rate. My savings account is 0.5%, my car loan is 5.5%, and my biggest credit card is 19%. These basically span the entire range of sensible interest rates (frankly 19% may even exceed that; that’s a doubling time of 3.6 years), and I know I’m not the exception but the rule.

So that’s the mess we’re in. Stay tuned; in future weeks I’ll talk about what we can do about it.